Figure 4 shows the design for a container in the shape of a hollow triangular prism. The container is open at the top, which is labelled ABCD.
The sides of the container, ABFE and DCFE, are rectangles.
The ends of the container, ADE and BCF, are congruent right-angled triangles, as
shown in Figure 4.
The ends of the container are vertical and the edge EF is horizontal.
The edges AE, DE and EF have lengths 4x metres, 3x metres and I metres
respectively.
Given that the container has a capacity of 0.75 m3 and is made of material of negligible
thickness, it can be shown that the internal surface area of the container, S m², is given
by
7
S = 12x2 +
8x
Sis a minimum when x = 0.332 m.
Using this value of x, find to 2 decimal places, the length of the edge CD.